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1. Motion Planning around Obstacles with Convex Optimization

   Tobia Marcucci, Mark Petersen2 ( May 2022 , ArXivorg)

   Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time. 

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2. Robust Optimization-based Motion Planning for high-DOF Robots under Sensing Uncertainty

   https://doi.org/10.1109/ICRA48506.2021.9560917  

   Quintero-Pena, Carlos ; Kyrillidis, Anastasios ; Kavraki, Lydia E. ( May 2021 , 2021 IEEE International Conference on Robotics and Automation (ICRA))

   null (Ed.)

   Motion planning for high degree-of-freedom (DOF) robots is challenging, especially when acting in complex environments under sensing uncertainty. While there is significant work on how to plan under state uncertainty for low-DOF robots, existing methods cannot be easily translated into the high-DOF case, due to the complex geometry of the robot’s body and its environment. In this paper, we present a method that enhances optimization-based motion planners to produce robust trajectories for high-DOF robots for convex obstacles. Our approach introduces robustness into planners that are based on sequential convex programming: We reformulate each convex subproblem as a robust optimization problem that “protects” the solution against deviations due to sensing uncertainty. The parameters of the robust problem are estimated by sampling from the distribution of noisy obstacles, and performing a first-order approximation of the signed distance function. The original merit function is updated to account for the new costs of the robust formulation at every step. The effectiveness of our approach is demonstrated on two simulated experiments that involve a full body square robot, that moves in randomly generated scenes, and a 7-DOF Fetch robot, performing tabletop operations. The results show nearly zero probability of collision for a reasonable range of the noise parameters for Gaussian and Uniform uncertainty. 

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3. Efficient Robot Motion Planning via Sampling and Optimization

   https://doi.org/10.23919/ACC50511.2021.9483146  

   Leu, Jessica ; Zhang, Ge ; Sun, Liting ; Tomizuka, Masayoshi ( May 2021 , 2021 American Control Conference (ACC))

   null (Ed.)

   Robot motion planning is one of the important elements in robotics. In environments full of obstacles, it is always challenging to find a collision-free and dynamically feasible path between the robot's initial configuration and goal configuration. While many motion planning algorithms have been proposed in the past, each of them has its pros and cons. This work presents a benchmark which implements and compares existing planning algorithms on a variety of problems with extensive simulation. Based on that, we also propose a hybrid planning algorithm, RRT*-CFS, that combines the merits of sampling-based planning methods and optimization-based planning methods. The first layer, RRT*, quickly samples a semi-optimal path. The second layer, CFS, performs sequential convex optimization given the reference path from RRT*. The proposed RRT*-CFS has feasibility and convergence guarantees. Simulation results show that RRT*-CFS benefits from the hybrid structure and performs robustly in various scenarios including the narrow passage problems. 

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4. Towards Robust Skill Generalization: Unifying Learning from Demonstration and Motion Planning

   Rana, M. A. ( October 2017 , Conference on Robot Learning)

   In this paper, we present Combined Learning from demonstration And Motion Planning (CLAMP) as an efficient approach to skill learning and generalizable skill reproduction. CLAMP combines the strengths of Learning from Demonstration (LfD) and motion planning into a unifying framework. We carry out probabilistic inference to find trajectories which are optimal with respect to a given skill and also feasible in different scenarios. We use factor graph optimization to speed up inference. To encode optimality, we provide a new probabilistic skill model based on a stochastic dynamical system. This skill model requires minimal parameter tuning to learn, is suitable to encode skill constraints, and allows efficient inference. Preliminary experimental results showing skill generalization over initial robot state and unforeseen obstacles are presented. 

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5. Robust planar dynamic pivoting by regulating inertial and grip forces

   Hou, Y. ; Jia, Z. ; Johnson, A.M. ; Mason, M.T. ( January 2020 , Algorithmic Foundations of Robotics XII)

   In this paper, we investigate the planar dynamic pivoting problem, in which a pinched object is reoriented to a desired pose through wrist swing motion and grip force regulation. Traditional approaches based on friction compensation do not work well for this problem, as we observe the torsional friction at the contact has large uncertainties during pivoting. In addition, the discontinuities of friction and the lower bound constraint on the grip force all make dynamic pivoting a challenging task for robots. To address these problems, we propose a robust control strategy that directly uses friction as a key input for dynamic pivoting, and show that active friction control by regulating the grip force significantly improves system stability. In particular, we embed a Lyapunov-based control law into a quadratic programming framework, which also ensures real-time computational speed and the existence of a solution. The proposed algorithm has been validated on our dynamic pivoting robot that emulates human wrist-finger configuration and motion. The object orientation can quickly converge to the target even under considerable uncertainties from friction and object grasping position, where traditional methods fail. 

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